document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523989>Question 523989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Flights of leaping animals typically have parabolic paths. The frog leaps on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 0.5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347517 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Flights of leaping animals typically have parabolic paths. The frog leaps on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 0.5.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard form of equation for parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex, A being a multiplier which affects the steepness or slope of the curve.<BR>\n" );
document.write( "Construct a parabola that opens downward as follows:<BR>\n" );
document.write( "Place the vertex at the origin (0,0)<BR>\n" );
document.write( "This makes the standard form: y=Ax^2<BR>\n" );
document.write( "Two ends of the parabola meet the ground at (-9/2,-3/2)(left side) and (9/2,-3/2)(right side)<BR>\n" );
document.write( "The problem is to find A<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Using the coordinates of the point where the parabola meets the ground on the right side.<BR>\n" );
document.write( "-3/2=A(9/2)^2<BR>\n" );
document.write( "-3/2=A(81/4)<BR>\n" );
document.write( "-12=162A<BR>\n" );
document.write( "A=-12/162=-1/13.5<BR>\n" );
document.write( "Equation: y=-x^2/13.5<BR>\n" );
document.write( "see graph below as a visual check<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2F13.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2F13.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );